On grid diagrams, braids and Markov moves

 

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dc.contributor.advisor Gay, David T en_ZA
dc.contributor.author Ayivor, Audry F en_ZA
dc.date.accessioned 2015-01-14T07:18:09Z
dc.date.available 2015-01-14T07:18:09Z
dc.date.issued 2010 en_ZA
dc.identifier.citation Ayivor, A. 2010. On grid diagrams, braids and Markov moves. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/12164
dc.description Includes abstract. en_ZA
dc.description Includes bibliographical references (leaves 42). en_ZA
dc.description.abstract Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Mathematics and Applied Mathematics en_ZA
dc.title On grid diagrams, braids and Markov moves en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Ayivor, A. F. (2010). <i>On grid diagrams, braids and Markov moves</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/12164 en_ZA
dc.identifier.chicagocitation Ayivor, Audry F. <i>"On grid diagrams, braids and Markov moves."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010. http://hdl.handle.net/11427/12164 en_ZA
dc.identifier.vancouvercitation Ayivor AF. On grid diagrams, braids and Markov moves. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2010 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/12164 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Ayivor, Audry F AB - Grid diagrams are essential in the new combinatorial version [MOST07] of the Heegaard Floer knot homology, and proving that these homologies are actually knot and link invariants depends on knowing that two grid diagrams representing isotopic links are related by grid moves. The purpose of this paper is to prove this fact. This result has already been proved by Cromwell [CrogS] and Dynnikov [Dyn06]. We present a new proof which is built upon Markov's theorem involving moves on braid words and link isotopy. DA - 2010 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2010 T1 - On grid diagrams, braids and Markov moves TI - On grid diagrams, braids and Markov moves UR - http://hdl.handle.net/11427/12164 ER - en_ZA


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